Noncommutative Geometry and Quantum Physics
Vietri sul Mare, August 31 - September 5, 2009
|
|
|
| Speaker: |
Gherardo Piacitelli, SISSA, Trieste |
| Title: |
Canonical Weyl Operators on the k-Minkowski Spacetime |
| Abstract: |
I will report on joint work with L. Dabrowski, where
we describe the canonical Weyl operators associated with the
coordinates of the k-Minkowski spacetime. They do not depend
on any arbitrary choice in the order of operator products, and
the resulting Weyl calculus is shown to be canonically associated to the
Lie algebra of the relations [u,vj]=vj, [vi,vj]=0.
I will give a fully detailed discussion in 1+1 dimensions, where
the operator trace of a quantised symbol also can be explicitly
written as a functional on the symbol itself.
The universal C*-algebra of the relations is shown to be
the direct sum of two copies of the algebra of compact operators and of
the abelian C*-algebra with spectrum R. The large k limit is the cartesian
product of a time line equipped with the usual topology, and a space
line where the origin 0 is an isolated point.
I also will describe pure states localised close to the space origin
with arbitrarily small precision in all the space and time coordinates.
|
|
 |
 |
G |
ruppo di |
R |
icerca |
E |
uropeo |
F |
ranco- |
I |
taliano in |
GE |
ometria |
N |
on |
CO |
mmutativa |
| roupement de |
echerche |
uropéen |
ranco |
talien en |
ométrie |
on |
mmutative |
|